Containment Control for a Social Network with State-Dependent Connectivity (.pdf)

[Big Fatty]

Containment Control for a Social Network with State-Dependent Connectivity

Zhen Kan, Justin Klotz, Eduardo L. Pasiliao Jr, Warren E. Dixon

1. Department of Mechanical and Aerospace Engineering,
   University of Florida, Gainesville, USA
2. Air Force Research Laboratory, Munitions Directorate,
   Eglin AFB, FL 32542, USA.

Abstract:
Social interactions influence our thoughts, opinions and actions. In
this paper, social interactions are studied within a group of
individuals composed of influential social leaders and followers. Each
person is assumed to maintain a social state, which can be an emotional
state or an opinion. Followers update their social states based on the
states of local neighbors, while social leaders maintain a constant
desired state. Social interactions are modeled as a general directed
graph where each directed edge represents an influence from one person
to another. Motivated by the non-local property of fractional-order
systems, the social response of individuals in the network are modeled
by fractional-order dynamics whose states depend on influences from
local neighbors and past experiences.  A decentralized influence method
is then developed to maintain existing social influence between
individuals (e.g., without isolating peers in the group) and to
influence the social group to a common desired state (e.g., within a
convex hull spanned by social leaders). Mittag-Leffler stability methods
are used to prove asymptotic stability of the networked fractional-order
system.

arxiv.org/pdf/1402.5644.pdf